Rotational mechanical systems and electrical analogs.

[peripatein]

Hi,

Homework Statement

Upon converting rotational mechanical components into their electrical analogs, one thing in particular baffles me. When is a rotational component converted into two sets of dependent sources and when is it converted into a single set? Let me try and clarify my question via a few examples.
In attachment 1, the pulley is converted into two sets of dependent sources: the first (v=ωR; τ₂=F₂R) is, I guess, the analog of the torque created by the rope pulled by F₂, whereas the second (ω=v₁/R; F₁=τ₁/R) is, I guess, the analog of the moment of inertia itself.
However, in attachment 2, a single set of dependent sources is used in the conversion. Why? What about the torque created by the pull of the rope? There seems to be some sort of discrepancy between the rationale behind this example and the one governing the first.
In attachment 3, J is converted into its analog - so far so good, but what about the force exerted by the strip which is under the wheel and which surely creates a torque?
Attachment 4 again shows no evidence of the supposedly expected analog of the torque created by the rope. Why?
Furthermore, why is B_s in attachment 4 in series whereas B₁ in attachment 3 is in parallel?
I'd sincerely appreciate some explanations on these delicate points.

 

[Valkarie]

Homework HelpWhen it comes to converting rotational mechanical components into their electrical equivalents, the primary things to consider are the moment of inertia and torque created by the rope. Generally speaking, when dealing with a mechanical system composed of two parts (e.g. a pulley with a rope), both parts should be converted into their respective electrical equivalent. For example, the pulley in attachment 1 is converted into two sets of dependent sources: one for the moment of inertia and one for the torque created by the rope. In attachment 2, however, only one set of dependent sources is used in the conversion - this is because the torque created by the rope is of a much lesser magnitude than the moment of inertia. Therefore, in this case, the torque created by the rope can be neglected, and only the moment of inertia needs to be accounted for. In attachment 3, J is converted into its electrical equivalent, but what about the force exerted by the strip which is under the wheel and which surely creates a torque? Well, in this case, the force exerted by the strip is not considered, as it is much smaller than the moment of inertia, and therefore can be neglected. Attachment 4 again shows no evidence of the supposedly expected analog of the torque created by the rope. This is because the torque created by the rope is much smaller than the moment of inertia, and thus can be neglected. Finally, the reason why Bs in attachment 4 is in series whereas B1 in attachment 3 is in parallel is because these two elements represent different types of components. Bs is a dependent source, and therefore must be placed in series, whereas B1 is an independent source, and thus must be placed in parallel.